Well, a dictionary is a handy reference to have, especially trying to discover the correct usage or meaning of a word.

For instance, a monitor, as used in computing, is a device used to display various computer generated information. The display is that part of the monitor which actually shows the information so that the user can read it. The screen also refers to this part of the monitor.

Things like windows and panes are referring to the different parts of what are termed "Graphical User Interfaces". Older interfaces are much simpler in design and operation and display only text with limited graphics. Typically, these older text based interfaces allowed only one process or program to run at a time, where GUIs were developed around the idea that several processes or programs could be running at once.

monitor = the physical object ... includes a screen, case, stand, cables, controls ... you get the idea.
display = the stuff being shown on the monitor "look at the display" - can refer to the screen (see below) but usually only when it is switched on.
screen = the front of the monitor where the display can be found
... these may all be used to refer to the physical object though
(i.e. "set up the screen over here" will probably mean the same thing as "set up the monitor over here".)

... these can also be technical terms in the programming language and/or the operating system.
For instance XOrg has configuration options for "device" (video card) "monitor" (the hardware) and "screen" (refers to the boundaries for graphics to be displayed).

The exact uses of the words will, therefore, depend on context - ain't English fun.

Since your interest is to use them correctly (there's no such thing as the "correct" usage, but we know what you mean :) ) rather than to understand them when others use them, then you will have to pay attention to the context and do a lot of pointing. Enjoy.

As decribed in earlier posts, "screen" can refer to the viewing portion of a monitor. Especially when the entire display is being used for a single application, "screen" can also refer to a particular content of a display, window, or pane. For example, you might "go to the User Profile Screen".